The invention relates generally to controlling power loss in a windfarm and more specifically to a system and method for distributing reactive load and windfarm voltage optimization for reduction of collector system losses.
Wind turbines are anticipated to becoming a progressively larger source of energy throughout the world, based on their capture of a renewable source of energy that does not emit carbon-based gases. However, wind turbine system development is still in the early stages relative to competing technologies. More specifically, system control for groups of jointly controlled wind turbines, or wind farms, is still in its infancy.
Current windfarm control techniques generally relate to voltage control and or real and reactive power control, either at the individual turbine or at a common collecting point for the system. Efficiency of the system, based on loss reduction, has generally not been considered in such control schemes.
The losses of a windfarm collector system are the sum of the ohmic load losses, proportional to the current magnitude squared, and the no-load excitation losses of the transformers in the collector system, which are proportional to the voltage raised to an exponent. This exponent is always greater than two. Empirically, the exponent is typically near three.
The load loss PLL(S,V), sometimes known as conduction loss or “copper” loss at any windfarm complex power output S and voltage V, is related to the load loss PLL-rated at the rated power output Srated and rated (nominal) voltage Vrated by Equation 1.
                                          P            LL                    ⁡                      (                          S              ,              V                        )                          =                                            (                                                V                  rated                                V                            )                        2                    ·                                    (                              S                                  S                  rated                                            )                        2                    ·                      P                          LL              -              rated                                                          Equation        ⁢                                  ⁢                  (          1          )                    
The no-load loss of the collector system transformers PNL(V), also called the excitation loss or “iron” loss, at any voltage V, is related to the no-load loss PNL-rated at rated voltage Vrated by the following:
                                          P            NL                    ⁡                      (            V            )                          =                                            (                              V                                  V                  rated                                            )                        N                    ·                      P                          NL              -              rated                                                          Equation        ⁢                                  ⁢                  (          2          )                    where N is an empirically derived exponent unique to the magnetic design and materials of the transformers used in the collector system.
The total loss PLOSS(S,V) at any voltage and complex power level is the sum of Equation (1) and (2), as described in Equation (3).
                                          P            LOSS                    ⁡                      (                          S              ,              V                        )                          =                                                            (                                                      V                    rated                                    V                                )                            2                        ·                                          (                                  S                                      S                    rated                                                  )                            2                        ·                          P                              LL                -                rated                                              +                                                    (                                  V                                      V                    rated                                                  )                            N                        ·                          P                              NL                -                rated                                                                        Equation        ⁢                                  ⁢                  (          3          )                    
The total loss can be minimized by optimized selection of V. This can be determined by differentiating Equation (3) with respect to V, and solving for the value of V where this first derivative is zero.
For typical parameters FIG. 1 shows the variation of total loss with voltage level for four different power levels. At 10% power, a low voltage is optimal. At 30% power, a voltage near the rated value is optimal, and above this power level, a high voltage is optimal from the standpoint of losses. The same information is shown in a 3-dimensional format in FIG. 2.
In addition to control solutions it would be possible to design a lower loss collector system by decreasing the collector system resistance (increase conductor cross sectional area) or designing a higher voltage collector system. These alternatives require substantial equipment investment and the savings in reduced losses generally do not justify the equipment investment.
Accordingly, there is a need to provide a method for system control to reduce losses through optimization of reactive load distribution and voltage control, while maintaining essentially the same physical equipment and control structure for the system.